I was about to type basically this. Brian's answer is a perfect answer to what the rules say that means shifts don't provoke opportunity attacks. Acedrummer_CLB's answer describes why this makes sense. Esentially a normal move involves 'walk fast through the fight and hope', letting people easily swing at you as you pass. A shift is a cautious sidestep while keeping your eyes on your opponents and your guard up (every martial art teaches how to do this in some way). So you move much more slowly, but don't leave openings.
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TynamNov 22 '10 at 14:39

Trigger: Opportunity actions allow you to take an action in response to an enemy letting its guard down. The one type of opportunity action that every combatant can take is an opportunity attack. Opportunity attacks are triggered by an enemy leaving a square adjacent to you or by an adjacent enemy making a ranged attack or an area attack.

This represents someone getting in a quick hit while the opposing creature is distracted.

However, the specific case of a shift 1 overrides the general. A shift is, flavourfully:

Moving through a fierce battle is dangerous; you must be careful to avoid a misstep that gives your foe a chance to strike a telling blow. The way you move safely when enemies are nearby is to shift.

With some other special notes about when it can be used. Thus, a shift is an action which uses the creature's move action on their turn, that explicitly limits distance moved (1 square) and what happens on that movement (no opportunity attacks.)

Then, the even more specific powers can override this more generalized definition for increased movement rates, usually during the course of a power.

The hierarchy of authority in this case, looks soemthing like the following:

Move Action: move on your turn
\-> Shift action: use your move to move one square without provoking
\-> Passing Attack (a fighter power): You can shift as part of the power

Using the specific to general overrides, we get: you can move 1(in this case) square (movement without provoking) as part of the power (movement without a move action) but you still must follow the rules for movement, such as staying on the ground.

The idea of exceptions is a bit hard to get used to if you're used to playing other editions of D&D. The consequence of "specific beats general" is that you only have to know your character's actions and the rules that they modify, such as shifting.

The overriding reason is that while Opportunity Attacks look great on paper, they're a pain in the ass in practice, so you need some way to be able to move and not get hit with them. Shifts are in place specifically to facilitate this.